2.0k words | Dan Hollick
Drawing curves.
Bézier curves compress a smooth shape into endpoints and control points that are easy for software to store and edit.
Bézier curves compress a smooth shape into endpoints and control points that are easy for software to store and edit. The apparent simplicity comes from a set of carefully chosen representations, transformations and physical assumptions working together.
Interpolation
The curve is calculated by repeatedly mixing points as a parameter moves from zero to one.
This is one part of a longer chain: anchor becomes control points becomes polynomial becomes curve. The useful abstraction hides the physical work, but the underlying constraints still shape the software built above it.
Handles
Control points pull the curve without usually sitting on the final path.
The implementation is full of compromises. Precision, speed, storage and energy rarely improve together, so practical systems choose the errors people are least likely to notice.
Continuity
Aligned handles create smooth joins; broken handles create deliberate corners.
Once this layer is visible, familiar design conventions stop looking arbitrary. They are accumulated responses to the capabilities and limits of the machinery below.
A visual study based on the original chapter. Text is condensed and rewritten.